Question: Solve for $x$ and $y$ using elimination. $\begin{align*}4x-6y &= 5 \\ -2x+6y &= 6\end{align*}$
Solution: We can eliminate $y$ when its corresponding coefficients are negative inverses. Add the top and bottom equations. $2x = 11$ Divide both sides by $2$ and reduce as necessary. $x = \dfrac{11}{2}$ Substitute $\dfrac{11}{2}$ for $x$ in the top equation. $4( \dfrac{11}{2})-6y = 5$ $22-6y = 5$ $-6y = -17$ $y = \dfrac{17}{6}$ The solution is $\enspace x = \dfrac{11}{2}, \enspace y = \dfrac{17}{6}$.